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Spring 2020 A Gröbner basis for the graph of the reciprocal plane
Alex Fink, David E. Speyer, Alexander Woo
J. Commut. Algebra 12(1): 77-86 (Spring 2020). DOI: 10.1216/jca.2020.12.77

Abstract

Given the complement of a hyperplane arrangement, let Γ be the closure of the graph of the map inverting each of its defining linear forms. The characteristic polynomial manifests itself in the Hilbert series of Γ in two different-seeming ways, one due to Terao and the other to Huh and Katz. We define an extension of the no broken circuit complex of a matroid and use it to give a direct Gröbner basis argument that the polynomials extracted from the Hilbert series in these two ways agree.

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Alex Fink. David E. Speyer. Alexander Woo. "A Gröbner basis for the graph of the reciprocal plane." J. Commut. Algebra 12 (1) 77 - 86, Spring 2020. https://doi.org/10.1216/jca.2020.12.77

Information

Received: 13 May 2017; Revised: 11 June 2017; Accepted: 18 June 2017; Published: Spring 2020
First available in Project Euclid: 13 May 2020

zbMATH: 07211326
MathSciNet: MR4097057
Digital Object Identifier: 10.1216/jca.2020.12.77

Subjects:
Primary: 05E45, 13F55, 13P10, 52C35

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.12 • No. 1 • Spring 2020
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